Proof That Being a T4 Space is a Topological Property
If a T4 spaceis homeomorphic to a spacethenis T4.
Ifis a T1 space homeomorphic to a spacethenis T1. Supposeis a normal space andis a homeomorphism. Letandbe disjoint closed subsets ofthen andare disjoint open sets of
Sinceis normal there are disjoint open setsandinsuch thatand
The setsandare open inandandhenceis normal and T4.